From repeated photoconductor testing: \(1\,\mathrm{kHz}\) and \(10\,\mathrm{kHz}\) were useful because they were measured consistently across devices. They are examples, not universal constants. The value comes from comparing the same lower and higher points under the same conditions.
A full noise spectrum contains far more information than two measurements. It can reveal the low-frequency rise, the flatter generation-recombination region, the GR rolloff, narrow interference peaks, and the eventual system or Johnson floor.
But repeated detector testing often produces noise values at the same small set of frequencies. A simple ratio can turn two routine measurements into a useful screening heuristic.
The ratio does not identify a microscopic mechanism. It answers a narrower question: is the lower-frequency noise elevated relative to a higher flat-band reference?
Noise amplitude spectral density at the lower frequency divided by the higher reference.
A ratio adds spectral shape to an absolute noise value
A noise value at \(f_H\) gives the detector's absolute noise level at that frequency. It does not show whether the spectrum remains flat as frequency decreases.
The ratio \(r_{L/H}\) adds that missing information:
Noise is approximately flat between the selected frequencies.
The lower-frequency point is elevated; low-frequency excess noise may be entering the test band.
The higher-frequency point is elevated; check interference, resonance, or another readout feature.
Always report the ratio with an absolute noise value
The minimum useful comparison is the pair \(\{e_n(f_H),\,r_{L/H}\}\). A ratio near unity does not mean the detector is quiet; it only means the two selected points are similar.
There is no universal pass/fail value. The most useful reference is usually the distribution produced by comparable detectors measured with the same procedure.
Two detectors can look equal at one frequency and very different at another
Suppose two detectors have nearly the same noise at the higher reference frequency. A single-frequency comparison would treat them as similar. At the lower frequency, however, one detector may remain nearly flat while the other is noticeably elevated.
| Detector | \(e_n(f_L)\)\(\mathrm{nV}/\sqrt{\mathrm{Hz}}\) | \(e_n(f_H)\)\(\mathrm{nV}/\sqrt{\mathrm{Hz}}\) | \(r_{L/H}\) | Immediate read |
|---|---|---|---|---|
| Detector A | 10.8 | 10.0 | 1.08 | Nearly flat |
| Detector B | 19.4 | 11.3 | 1.72 | Low-frequency rise |
Worked calculation
The two detectors have similar noise at \(f_H\), but Detector B rises much more strongly toward \(f_L\). The ratio exposes that difference immediately.
The ratio is particularly useful across detector populations, where it can identify outliers that deserve a full frequency sweep.
A difference from unity must exceed measurement variation
Interpret \(r_{L/H}-1\) relative to repeated measurements. A small departure from unity is not physically meaningful when it is comparable to drift, temperature variation, bias instability, or the statistical spread of the noise estimate.
For screening work, report the mean ratio, the spread across repeats, and the number of measurements. Population limits should come from comparable detectors measured with the same procedure—not from a universal threshold.
Optional uncertainty propagation
If the two noise estimates are treated as independent, a first-order estimate is
\[ \left(\frac{\sigma_r}{r_{L/H}}\right)^2\approx \left(\frac{\sigma_L}{e_n(f_L)}\right)^2+ \left(\frac{\sigma_H}{e_n(f_H)}\right)^2. \]Use the actual repeatability data when the two measurements share correlated drift or common calibration errors.
The frequencies are chosen by function, not by convention
The method is general. Use a lower comparison frequency \(f_L\) and a higher reference frequency \(f_H\). Under a healthy baseline, both points should lie in the established flat GR measurement region. The heuristic becomes useful when excess low-frequency noise raises \(e_n(f_L)\) while \(e_n(f_H)\) remains a stable reference.
Higher reference: \(f_H\)
Choose a point in the established flat GR region, below detector or readout rolloff and away from isolated interference.
Lower comparison: \(f_L\)
Choose a lower point that is normally still in the flat region, but close enough to the low-frequency side to respond when the low-frequency crossover shifts upward.
In repeated photoconductor measurements, \(1\,\mathrm{kHz}\) and \(10\,\mathrm{kHz}\) are convenient examples. Their usefulness comes from repeatability and their location in the measurement band—not from any fundamental property of those exact values.
Important: the ratio does not require an exact \(1/f\) law. Two measured points are compared directly; no spectral exponent is assumed.
The ratio is related to the low-frequency crossover
Use \(f_{\times}\) for the crossover between a fitted low-frequency excess-noise trend and the flat GR reference level. For a noise amplitude spectral density fit, write the low-frequency branch as \(e_n(f)=A f^{-\beta}\), where \(A\) and \(\beta\) are obtained from the measured spectrum rather than assumed.
The two-frequency heuristic does not measure \(f_{\times}\). It flags when the crossover may have moved high enough to affect the lower comparison point:
- If \(f_{\times}\ll f_L\), both selected points may remain in the flat region and \(r_{L/H}\approx 1\).
- If \(f_{\times}\) approaches or exceeds \(f_L\), \(e_n(f_L)\) can rise while \(e_n(f_H)\) remains a useful reference, producing \(r_{L/H}>1\).
- A full spectrum is still required to distinguish a broad low-frequency rise from narrowband interference or another frequency-dependent process.
This is why the ratio works as a screening quantity: it does not replace the spectrum; it identifies which devices deserve a full sweep.
Use the ratio as a population variable, not a universal MCT specification
Best use in HgCdTe photoconductors
Track \(r_{L/H}\) together with \(e_n(f_H)\) across passivation conditions, wafer position, device geometry, bias, temperature, and fabrication lot. A shift in the population distribution is more informative than an isolated value from one detector.
Published HgCdTe photoconductor measurements have shown that low-frequency noise can depend strongly on passivation and inferred surface-trap density. That supports using an elevated ratio as a screening flag, but it does not make the ratio a unique diagnosis of surface noise. [1]
What an elevated ratio may flag
An unusually large ratio within a comparable detector population can be consistent with several device or measurement problems:
Surface and fabrication
- passivation changes;
- surface or interface traps;
- process damage or nonuniformity.
Device and operating point
- contact-related fluctuations;
- current crowding;
- bias dependence or self-heating.
Measurement system
- slow thermal drift;
- bias-source contamination;
- pickup or readout features.
The ratio is a flag, not a diagnosis. Bias sweeps, temperature dependence, full spectra, geometry comparisons, contact studies, and passivation experiments are what separate the possible causes.
The ratio is only useful when both points belong to the detector
Keep the test chain quieter than the device.
Both values must be noise amplitude spectral densities normalized with the correct ENBW; raw RMS values are not directly comparable. Hold detector temperature, bias, resistance, optical condition, preamplifier gain, and averaging procedure constant. Battery-based bias, an appropriately matched low-noise preamplifier, short shielded wiring, disciplined grounding, and a Faraday cage help keep bench noise below the detector.
These controls do not define \(r_{L/H}\). They determine whether the ratio reflects detector behavior rather than the measurement system.
A compact comparison record
A useful record contains the two measured noise densities, their ratio, and enough operating information to reproduce the comparison:
Always report the absolute reference noise \(e_n(f_H)\) with the ratio. When \(1\,\mathrm{kHz}\) and \(10\,\mathrm{kHz}\) are used, report those values explicitly; do not present them as universal detector standards.
Bottom line: a two-frequency ratio is a fast, repeatable heuristic for identifying photoconductors whose low-frequency excess noise reaches farther into the normal test band than it does in comparable devices.
References and further reading
- C. T. Lin, Y. K. Su, S. J. Chang, H. T. Huang, S. M. Chang, and T. P. Sun, “Effects of passivation and extraction surface trap density on the 1/f noise of HgCdTe photoconductive detector,” IEEE Photonics Technology Letters, vol. 9, no. 2, pp. 232–234, 1997. doi:10.1109/68.553102.
- National Institute of Standards and Technology, “Flicker Noise,” Time and Frequency from A to Z. NIST definition and terminology.
- Zurich Instruments, “Lock-in Tab,” UHF User Manual. The manual distinguishes noise-equivalent power bandwidth from the \(3\,\mathrm{dB}\) bandwidth and documents filter settings relevant to noise normalization. Instrument documentation.
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